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Mean Squared Error (MSE):
- Calculates the average of the squared differences between predicted and actual values.
- Larger errors contribute more to the overall error.
- The formula for MSE is: [ MSE = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 ]
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Mean Absolute Error (MAE):
- Calculates the average of the absolute differences between predicted and actual values.
- Treats all errors equally, regardless of magnitude.
- The formula for MAE is: [ MAE = \frac{1}{n} \sum_{i=1}^{n} |y_i - \hat{y}_i| ]
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Root Mean Squared Error (RMSE):
- The square root of the mean squared error.
- Provides an interpretable scale because it's in the same units as the target variable.
- The formula for RMSE is: [ RMSE = \sqrt{MSE} ]
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R-squared (R2) Score:
- Measures the proportion of the variance in the dependent variable that is predictable from the independent variables.
- Ranges from 0 to 1, where 1 indicates a perfect fit.
- The formula for R2 is: [ R^2 = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}i)^2}{\sum{i=1}^{n} (y_i - \bar{y})^2} ] where (\bar{y}) is the mean of the target variable.
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Mean Squared Logarithmic Error (MSLE):
- Measures the average of the logarithmic differences between predicted and actual values.
- Particularly useful when the target variable spans multiple orders of magnitude.
- The formula for MSLE is: [ MSLE = \frac{1}{n} \sum_{i=1}^{n} (\log(1 + y_i) - \log(1 + \hat{y}_i))^2 ]
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Mean Bias Deviation (MBD):
- Measures the average relative difference between predicted and actual values.
- Positive values indicate overestimation, and negative values indicate underestimation.
- The formula for MBD is: [ MBD = \frac{1}{n} \sum_{i=1}^{n} \frac{y_i - \hat{y}_i}{y_i} \times 100% ]
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Explained Variance Score:
- Measures the proportion to which the model explains the variance of the target variable.
- Ranges from 0 to 1, where 1 indicates a perfect explanation.
- The formula for explained variance is: [ \text{Explained Variance} = 1 - \frac{\text{Var}(y - \hat{y})}{\text{Var}(y)} ]